In this thesis, we investigate several key results in the canon of metamathematics, applying
the contemporary perspective of formalisation in constructive type theory and mechanisation …

Dependent types are a powerful tool for maintaining program invariants. To take advantage
of this aspect in real-world programming, efforts have been put into enriching dependently …

A class of models is presented, in the form of continuation monads polymorphic for first-order
individuals, that is sound and complete for minimal intuitionistic predicate logic (including …

Negation is not involutive in the λC calculus because it does not distinguish captured stacks
from continuations. We show that there is a formulae-as-types correspondence between the …

The paper is a contribution to intuitionistic reverse mathematics. We work in a weak formal
system for intuitionistic analysis. The Principle of Open Induction on Cantor space is the …

We revisit the notion of intuitionistic equivalence and formal proof representations by
adopting the view of formulas as exponential polynomials. After observing that most of the …

Markov's principle is a statement that originated in the Russian school of Constructive
Mathematics and stated originally that" if it is impossible that an algorithm does not …

We construct a partially-ordered hierarchy of delimited control operators similar to those of
the CPS hierarchy of Danvy and Filinski [5]. However, instead of relying on nested CPS …

In the earlier papers [30],[31] and [32] we collected statements that are, in a weak formal
context, equivalent to Brouwer's Fan Theorem. This time, we do the same for the Principle of …

We present an implementation in the Coq proof assistant of type directed partial evaluation
(TDPE) algorithms for call-by-name and call-by-value versions of shift and reset delimited …